Parametric instability of steady fluid flow in a corrugated pipe

TL;DR

This paper investigates the parametric instability of steady ideal fluid flow in corrugated pipes, revealing that certain frequency bands induce instability even at zero flow velocity, with stability diagrams computed numerically.

Contribution

It introduces a first-order perturbation analysis of flow stability in corrugated pipes and provides numerical stability diagrams across various parameters.

Findings

Parametric instability occurs in specific frequency bands.

Instability can occur even with zero base flow velocity.

Higher-order instability bands depend on flow velocity.

Abstract

In this paper, we show that the quasi-one-dimensional flow of an ideal inviscid fluid in a corrugated pipe is parametrically unstable in certain frequency bands. First-order perturbation theory is used to analyze the stability of the flow, and shows that parametric instability occurs even if the velocity of the base flow is zero. Stability diagrams of the system as a function of the amplitude and period of the corrugation, for different velocities of the base flow, are obtained using parallel numerical computation. The analysis shows that the higher-order bands of instability are strongly dependent on the base flow velocity.